Easter & Hitzer: Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2

Robert B. Easter, Eckhard Hitzer, Conic and Cyclidic Sections in Double Conformal Geometric Algebra G8,2, Proceedings of conference SSI 2016, Session SS11, pp. 866-871, 6-8 Dec. 2016, Otsu, Shiga, Japan.

Preprint for free download (PDF): http://vixra.org/pdf/1612.0221v1.pdf

Abstract: The G_{8,2} Geometric Algebra, also called the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), has entities that represent conic sections. DCGA also has entities that represent planar sections of Darboux cyclides, which are called cyclidic sections in this paper. This paper presents these entities and many operations on them. Operations include rejection, projection, rejection, and intersection with respect to spheres and planes. Other operations include rotation, translation, and dilation. Possible applications are introduced that include orthographic and perspective projections of conic sections onto view planes, which may be of interest in computer graphics or other computational geometry subjects.

Keywords: conformal geometric algebra, conic sections, perspective projection


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